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If DeltaABC~DeltaPQR with (BC)/(QR)=1/3,...

If `DeltaABC~DeltaPQR` with `(BC)/(QR)=1/3`,then `(ar(DeltaPRQ))/(ar(DeltaBCA))` is equal to

A

`9/1`

B

`3/1`

C

`1/3`

D

`1/9`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `DeltaABC~DeltaPQR` and `(BC)/(QR)=1/3`
We know that, the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides.
`therefore(ar(DeltaPRQ))/(ar(DeltaBCA))=((QR)^(2))/((BC)^(2))=((QR)/(BC))^(2)`=(3/1)^(2)=9/1=9`
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